FIG. 1 shows a typical constant-current power supply circuit of the band-gap type and a minute constant-current power supply circuit, which have been conventionally used.
In FIG. 1, Q1 through Q10 are transistors, and R1 through R3 are resistors. Transistor Q1 and transistor Q2 are of the same standard, and transistor Q1 has a parallel connected arrangement the number of which is represented by n, and generates a band-gap voltage. Further, transistors Q4 through Q8 constitute a current Miller constant-current circuit. In this circuit, the following equations hold: EQU V.sub.BE (Q2)-V.sub.BE (Q1)=I(Q1).times.R1, EQU V.sub.T ln(I(Q2)/I.sub.S)-V.sub.T ln(I(Q1)/n.multidot.I.sub.S)=I(Q1).times.R1, EQU V.sub.T ln(I(Q2).multidot.n/I(Q1).times.R1,
where V.sub.BE ( ) represents a base-emitter voltage of the transistor that is denoted by a sign seen inside the parentheses ( ); I( ) represents a current at the emitter of the transistor that is denoted by a sign seen inside the parentheses ( ); and R1 represents a value of resistivity of resistor R1. Further, V.sub.T =kT/q (k: Boltzmann's constant, q: electrical charge, T: absolute temperature), and I.sub.S represents a reverse-directional saturated current of the transistor.
Here, I(Q4)=I(Q5) and I(Q1).congruent.I(Q2) virtually hold because of the current Miller circuit consisted of transistors Q4 and Q5.
Therefore, EQU I(Q1)=(V.sub.T / R1)ln. (1)
Here, for example, letting R1=6 K.OMEGA. and n=10, V.sub.T .congruent.26 mV holds; therefore, the following equation holds between I(Q1) and I(Q4): EQU I(Q4).congruent.I(Q1)=10 .mu.A.
Transistors Q7 through Q10 and resistor R2 constitute a constant-current power supply circuit for generating a constant current I.sub.out that is smaller than the value of the current Miller current I(Q4) by one or two figures. The following equations hold in this circuit: EQU V.sub.BE (Q7)-V.sub.BE (Q8)=I(Q10).times.R2, EQU V.sub.T ln(I(Q7)/I.sub.S)-V.sub.T ln(I(Q8)/I.sub.S)= I(Q10).times.R2, EQU V.sub.T ln(I(Q7)/I(Q8))=I(Q10).times.R2, EQU I(Q7)/I(Q8)=exp(I(Q10).times.R2/V.sub.T).
Therefore, EQU I.sub.out =I(Q8)=I(Q7)/exp(I(Q10).times.R2/V.sub.T). (2)
Here, the above equations hold on condition that: EQU I.sub.out &lt;I(Q10).
Letting I(Q4)=10 .mu.A, m=1 and R2=12 K.OMEGA., EQU I(Q10)/m=I(Q7)=I(Q4)=10 .mu.A, EQU I.sub.out .congruent.10 .mu.A/exp(120 mV/26 mV).congruent.10.mu.A/100=0.1.mu.A.
As described above, a circuit for supplying a minute constant current in constituted based on the constant-current power supply circuit of the band-gap type that is capable of supplying a comparatively stable constant current in spite of variations of temperatures and source voltage.
Next, FIG. 4 shows another typical constant-current power supply circuit of the band-gap type, which have been used conventionally. In FIG. 4, Q21 through Q27 are transistors, and R20 and R22 through R26 are resistors. The base of transistor Q21 is connected to its own collector and the base of transistor 22, and the emitter of transistor Q21 is connected to ground via resistor R20, while the collector of transistor Q21 is connected to the collector of transistor Q24.
The emitter of transistor Q22 is connected to the emitter of transistor Q23 via resistor R22, while the collector of transistor Q22 is connected to the base of transistor Q23 as well as to the collector of transistor Q25. The collector of transistor Q23 is connected to the base and the collector of transistor Q26 as well as to the bases of transistors Q24, Q25, and Q27. The emitters of transistors Q24, Q25, Q26 and Q27 are connected to Vcc (power source input terminal) respectively via resistors R23, R24, R25 and R26.
Thus, an output current I.sub.out is obtained from the collector of transistor Q27. Additionally, transistor Q21 is constituted of transistors, each having the same configuration as transistor Q22, which are connected in parallel with one another, and the number of which is denoted by n. Transistor Q21 thus generates a band-gap voltage. Further, a current Miller constant-current power supply circuit is constituted by transistors Q24 through Q27.
As with the circuit shown in FIG. 1, the following equations hold in the circuit of FIG. 4. EQU V.sub.BE (Q22)-V.sub.BE (Q21)=I(Q21).times.R20, (3) EQU V.sub.T .times.ln(I(Q22)/I.sub.S)-V.sub.T .times.ln(I(Q21)/(I.sub.S .times.n)=I(Q21) .times.R20.
Therefore, EQU V.sub.T .times.ln n(I(Q22)/I(Q21))=I(Q21).times.R20, (4)
where V.sub.BE ( ) represents base-emitter voltage of the transistor that is denoted by a sign seen inside the parentheses ( ); I( ) represents an emitter current in the transistor that is denoted by a sign seen inside the parentheses ( ); and R20 represents a value of resistivity of resistor R20. Further, V.sub.T =kT/q (k: Boltzmann's constant, q: electrical charge, T: absolute temperature), and I.sub.S represents a reverse- directional saturated current of the reference transistor Q22.
Here, the collector current of transistor Q27 that constitutes the current Miller constant-current power supply circuit, that is, the output current I.sub.out is given by: I.sub.out =I.sub.co (Q24)=I.sub.co (Q25) (where Ico( ) represents a collector current of the transistor that is denoted by a sign seen inside the parentheses ( )). In this case, it is considered that I.sub.out .congruent.I(Q21).congruent.I(Q22); therefore, the equation (4) is rearranged as follows: EQU V.sub.T .times.ln n=I.sub.out .times.R20, (5 )
Therefore, EQU I.sub.out =(V.sub.T / R20)ln n, (6)
Here, for example, letting R20=6 K.OMEGA. and n=10, .sub.I.sub.out is given by: EQU I.sub.out .congruent.10.mu.A.
As described above, the constant-current power supply circuit of the band-gap type shown in FIG. 4 is capable of supplying a comparatively stable constant current in spite of variations of temperatures and source voltage. Here, the temperature characteristic of the circuit is approximately +3000 ppm/.degree. C. The reason that the stable constant current is supplied in spite of variations of temperatures and source voltage is because the collector voltages of transistor Q21 and transistor Q22 are always kept at virtually the same voltage and the influence of the Early effect is thus extremely small.
Most of ICs (Integrated Circuits) adopt a constant-current power supply circuit of the band-gap type as a current source, as shown in FIG. 1 and FIG. 4. This is because the constant-current power-supply circuit that requires only a comparatively small current value can be constructed by using resistor R1(R20) having a comparatively small value of resistivity, such as several K.OMEGA. in the value of resistivity R1(R20). Further, with the above-mentioned circuit configuration, it is possible to construct a constant-current power supply circuit for generating a constant current that is smaller than the value of the current Miller current by one or two figures by the use of resistors ranging from several K.OMEGA. to several tens K.OMEGA..
The resulting constant current is made to be independent of V.sub.BE by constructing the transistor using repeated patterns, and the influence of h.sub.FE on the current is suppressed to a minimal level with an appropriate circuit configuration. However, as is understood by equation (1) or equation (6), the current value of the constant current is determined by the value of resistivity R1(R20) of resistor R1(R20). This has arisen a disadvantage that if the value of resistivity deviates from a design value due to process deviations which occur during the IC production, the current value of the constant current will fluctuate.
The process deviations of ICs are mainly classified into two types: One type of them, which is generally called "relative deviation", is caused by the fact that characteristics in each individual IC chip shift as a whole in a certain direction and the amount of the shift deviates depending on the respective chips (or wafers). This relative deviation can be virtually solved by installing as closely as possible devices that require conformity in characteristics with one another in their circuit operation.
As to the other type of the process deviations, that is,"absolute deviation", in the case where a constant current that has been generated by the constant-current power supply circuit of the band-gap type is applied to a resistor as a load that has the same configuration as that of resistor R1(R20), and the resulting voltage V.sub.out is utilized in the following step or released to an external device, the influence of absolute deviation on the values of resistivity is hardly found because the values of resistivity deviate at the same rate and cancel each other. However, in the case where the current I.sub.out is utilized or released as a constant current, the current value deviates in response to the shifted amount of the value of resistivity.
As to absolute deviations of resistors used in an IC, there are two types of them: one is deviation on sheet resistivity that is caused by deviations of the densities of impurities to be injected to produce a resistor; and the other is line-width deviation of resistors that is caused by deviations of etching time, etc. on oxide films that determine the shape of a resistor to be formed. These two types of deviations occur as individual phenomena.
Additionally, in the output circuit of the minute constant current, the current I.sub.out also deviates in response to absolute deviation on the value of resistivity because it is produced based on a current generated by the constant-current power supply circuit of the band-gap type.